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# Total internal reflection & Critical Angle

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### Total internal reflection & Critical Angle

1. 1. TOTAL INTERNAL REFLECTION and the CRITICAL ANGLE
2. 2. TOTAL INTERNAL REFLECTION <ul><li>The inside surface of water or a glass block can act like a mirror. </li></ul>
3. 3. Total Internal Reflection <ul><li>Occurs when light reflects off of the inside wall of a denser medium (higher index of refraction ) </li></ul>
4. 4. Total Internal Reflection <ul><li>Recall: </li></ul><ul><li>When light passes from a dense material into a less dense medium, light reflects away from the normal </li></ul>
5. 5. Total Internal Reflection <ul><li>As the angle of incidence increases , </li></ul><ul><li>the angle of refraction increases </li></ul>
6. 6. Critical Angle <ul><li>At a certain angle, the refracted ray follows a path exactly along the surface of the dense medium </li></ul><ul><li>When the angle of refraction is at 90 o the incident angle is called the “ critical angle ” </li></ul>
7. 7. Critical Angle <ul><li>Critical angle is the angle at which the refracted ray is at 90 o </li></ul>
8. 8. Critical Angle determines Total Internal Reflection <ul><li>If the incident ray is increased beyond the critical angle, the light is no longer refracted </li></ul><ul><li>Instead, it is reflected back inside the medium </li></ul><ul><li>This is called “ total internal reflection ” </li></ul><ul><li>When incident angle is greater than the critical angle (i>C), there is no refracted rays, all emergent rays are internally reflected </li></ul>
9. 9. TOTAL INTERNAL REFL E CTION A light ray hits the inside face of a semicircular block.
10. 10. Total Internal Reflection <ul><li>A light ray hits the inside face of a semicircular block as follows. </li></ul><ul><li>What will happen as the angle of incidence increases? </li></ul>air glass incident ray reflected ray refracted ray
11. 11. Total Internal Reflection air glass incident ray reflected ray refracted ray
12. 12. Total Internal Reflection air glass incident ray reflected ray refracted ray
13. 13. Total Internal Reflection air glass incident ray reflected ray refracted ray
14. 14. Total Internal Reflection air glass incident ray reflected ray
15. 15. Total Internal Reflection <ul><li>What happened? </li></ul>air glass incident ray reflected ray refracted ray air glass incident ray reflected ray
16. 16. Total Internal Reflection <ul><li>At a small angle of incidence: </li></ul><ul><li>Incident ray splits into refracted & reflected </li></ul><ul><li>Angle of refraction < 90 o </li></ul><ul><li>Angle of reflection = angle of incidence </li></ul>air glass incident ray reflected ray refracted ray
17. 17. Total Internal Reflection <ul><li>As the angle of incidence increases, the angle of refraction increases until… </li></ul>air glass incident ray reflected ray refracted ray
18. 18. Total Internal Reflection <ul><li>Angle of refraction is at 90 o , parallel to the surface of the medium </li></ul><ul><li>At this point the angle of incidence = critical angle (C) </li></ul><ul><li>Angle of incidence = C when angle of refraction = 90 o </li></ul>air glass incident ray reflected ray refracted ray
19. 19. Total Internal Reflection <ul><li>As the angle of incidence increase beyond the critical angle (>C), there is no more refracted ray </li></ul><ul><li>All emergent rays are totally reflected inside the medium = Total Internal Reflection (TIR) </li></ul>air glass incident ray reflected ray
20. 20. Conditions for TIR & Critical Angle <ul><li>Light is traveling slower in the first medium than in the second medium (v 1 < v 2 ) </li></ul><ul><li>Thus light is moving from medium of higher refractive index to one of lower refractive index (n 1 > n 2 ) </li></ul><ul><li>Critical angle (C) is defined when the angle of refraction is 90 o to the normal (  2 = 90 o ) </li></ul><ul><li>TIR occurs when angle of incidence is larger than the critical angle (  1 > C) </li></ul>air glass incident ray reflected ray
21. 21. Calculating Critical Angle <ul><li>Snell’s Law: n 1 sin  1 = n 2 sin  2 </li></ul><ul><li>Critical angle C =  1 thus solve for  1 </li></ul><ul><li>At the critical angle, the refracted ray is a 90 o =  2 </li></ul><ul><li>n 1 sin  1 = n 2 sin 90 o ( sin 90 o = 1 ) </li></ul><ul><li>n 1 sin  1 = n 2 1 </li></ul><ul><li>n 1 sin  1 = n 2 </li></ul><ul><li>Rearrange equation to get: </li></ul><ul><li>sin  1 = n 2 / n 1 </li></ul><ul><li> 1 = sin -1 (n 2 / n 1 ) </li></ul><ul><li>If medium 2 = air, then n 2 = 1 </li></ul><ul><li> 1 = sin -1 ( 1 / n 1 ) </li></ul><ul><li>C = sin -1 (1 / n 1 ) </li></ul>air glass C =  1 r refracted ray reflected ray incident ray R =  2
22. 22. TOTAL INTERNAL REFLECTION <ul><li>critical angles of different materials </li></ul>Medium Refractive index Critical angle 1.50–1.70 30  –42  Glass Water Perspex Diamond 1.33 49  1.5 42  2.42 24 
23. 23. TIR in Diamonds <ul><li>Sparkling is due to: </li></ul><ul><li>Cut of diamond faces </li></ul><ul><li>High index of refraction which means a very small critical angle (n = 2.42, C = 24.4°) </li></ul><ul><li>Incident rays can undergo multiple TIR inside a diamond before exiting the top of the diamond. </li></ul>
24. 24. TIR in Fiber Optics <ul><li>Technology that uses light to transmit information along glass cables </li></ul><ul><li>Fibre optics cable is made up of a bundle of glass fibres </li></ul><ul><li>Sample materials: high-purity glass, Lucite </li></ul>
25. 25. TIR in Fiber Optics <ul><li>Fiber optics cable has a small critical angle, thus a high refractive index </li></ul><ul><li>Light entering will always have an angle of incidence greater than the critical angle </li></ul>
26. 26. TIR in Fiber Optics <ul><li>Light does not escape as it travels along the fiber optics cable because it undergoes total internal reflection </li></ul>http://ecademy.agnesscott.edu/~asullivan/Pictures/TIR.jpg
27. 27. TIR in Fiber Optics
28. 28. TIR in Fiber Optics <ul><li>Advantages of Fiber Optics </li></ul><ul><li>Signals are not affected by electrical storms. </li></ul><ul><li>Cable is smaller and lighter than copper cable. </li></ul><ul><li>More signals can be carried over longer distances. </li></ul>
29. 29. <ul><li>An endoscope is a flexible fibre optic cable through which internal cavities can be viewed. </li></ul><ul><li>Routinely used in the diagnosis of cancer and ulcers. </li></ul>Fiber Optics in Endoscopes http://marylandcolonoscopy.com/wp-content/uploads/2010/05/CDR0000433287.jpg
30. 30. Gastroscopy <ul><li>Endoscopy examination of a stomach </li></ul><ul><li>Endoscope inserted through the patient's mouth and fed down through throat </li></ul><ul><li>Image obtained by endoscope is projected onto a screen </li></ul><ul><li>A surgical instrument for obtaining a biopsy has been fed through the endoscope cable and controlled by the doctor </li></ul>http://www.sciencephoto.com/media/272329/enlarge
31. 31. Digestive Endoscopy <ul><li>http://www.sciencephoto.com/media/126772/enlarge </li></ul>
32. 32. Diagnosing Cancer <ul><li>Doctors using a fibroscope to investigate suspected lung cancer in a patient's bronchi (airways). A fibroscope is a flexible fibre optic cable with a camera on the end, similar to an endoscope. </li></ul>Photographed in Belgium. http://www.sciencephoto.com/media/137299/enlarge
33. 33. TIR in Prisms <ul><li>Plane mirror = glass + silvered surface </li></ul><ul><li>multiple reflection inside the glass </li></ul><ul><li>multiple images formed </li></ul><ul><li>nuisance in optical instruments </li></ul>glass sheet silvered surface I 1 I 2 I 3 Object
34. 34. Prisms <ul><li>If light rays strike the inside face at an angle > 42  , glass prism behaves like a perfect mirror. </li></ul><ul><li>Prisms are more useful than mirrors because it reflects almost 100% of light internally. Mirrors lose some light through absorption. </li></ul><ul><li>Emergent can be 90 o or 180 o relative to incident ray. </li></ul>45  45  45  45  45  45 
35. 35. Prisms in Periscopes <ul><li>Instrument for observation from a concealed position </li></ul><ul><li>Uses two triangular prisms (or mirrors) to change direction of light by 90 o </li></ul><ul><li>Used in war and in submarines </li></ul>
36. 36. In War <ul><li>Land Periscope used by a German Staff Officer during 1914 </li></ul><ul><li>Lens was sixteen feet above the ground, protecting the officer from enemy observation. </li></ul>http://www.historyofwar.org/Pictures/pictures_periscope_land.html
37. 37. http://www.history.navy.mil/photos/images/i02000/i02649.jpg
38. 38. Submarines <ul><li>American submarine commander inspects the horizon through the periscope (1942) </li></ul>http://mg-34.com/index.php/photo-19391945/1574-the-commander-of-the-submarines-periscope-looks
39. 39. http://web.mst.edu/~rogersda/military_service/periscopes.jpg Submarines carry all kinds of extendable devices in their sail which allow them to sense above the ocean's surface. This shows a deployed periscope (on left) and other electronic surveillance and communications probes.
40. 40. Prisms in Binoculars <ul><li>Uses 2 prisms to change direction of light by 180 o </li></ul>
41. 41. Prisms in Single-lens Camera <ul><li>A five-sided ‘ pentaprism ’ reflects light from the mirror into the eye. </li></ul>film mirror
42. 42. Prisms and Retro-reflectors <ul><li>Device that returns incident light back in exactly the same direction from which it came </li></ul><ul><li>Applications in bike reflectors, reflective strip on clothing, road signs </li></ul>45  45  45 
43. 43. Practice Problems <ul><li>A ray of light traveling in the direction EO in air enters a rectangular block at an angle of incidence = 30  . The resulting angle of refraction = 18  . </li></ul><ul><li>a. Find the refractive index n of the block. </li></ul>30  18  E O
44. 44. Practice Problems <ul><li>Given:  1 = 30  ,  2 = 18  , n 1 (air) = 1 </li></ul><ul><li>Required: n 2 (block) </li></ul><ul><li>Analysis: n 1 sin  1 = n 2 sin  2 </li></ul><ul><li>Solution: </li></ul><ul><li>1 x sin 30  = n 2 sin 18  </li></ul><ul><li>n 2 = sin 30  / sin 18  = 1.62 </li></ul><ul><li>Phrase: </li></ul><ul><li>The index of refraction of the block is 1.62 </li></ul>30  18  E O
45. 45. Practice Problems <ul><li>b. Find the critical angle C for the block. </li></ul>Recall: If medium 2 = air, then C =  1 = sin -1 (1 / n 1 ) 30  18  E O
46. 46. Practice Problems <ul><li>b. Find the critical angle C for the block. </li></ul><ul><li>Given:  2 = 90  , n 2 (air) = 1, n 1 (block) = 1.62 </li></ul><ul><li>Required:  1 </li></ul><ul><li>Analysis: n 1 sin  1 = n 2 sin  2 </li></ul><ul><li>Solution: </li></ul><ul><li>1.62 x sin  1 = 1 x sin 90  </li></ul><ul><li>sin  1 = 1 / 1.62 </li></ul><ul><li> 1 = sin -1 ( 1 / 1.62) = 38.1  </li></ul><ul><li>Phrase: </li></ul><ul><li>The critical angle of the block is 38.1  </li></ul>Recall: If medium 2 = air, then C =  1 = sin -1 (1 / n 1 ) 30  18  E O
47. 47. Practice Problems <ul><li>c. If the ray is incident on surface BC , from which surface and at what angle will the ray leave the block? </li></ul>30  A B C D
48. 48. Practice Problems <ul><li>c. If the ray is incident on surface BC , from which surface and at what angle will the ray leave the block? </li></ul><ul><li>Given: </li></ul><ul><li> 1 = 60  </li></ul><ul><li>n 1 (air) = 1 </li></ul><ul><li>n 2 (block) = 1.62 </li></ul><ul><li>Required:  2 </li></ul><ul><li>Analysis: </li></ul><ul><li>n 1 sin  1 = n 2 sin  2 </li></ul><ul><li>Solution: </li></ul><ul><li>1 x sin 60  = 1.62 x sin  2 </li></ul><ul><li>sin  2 = 1 x sin 60  / 1.62 </li></ul><ul><li> 2 = sin -1 ( 1 x sin 60  / 1.62) = 32.3  </li></ul>30  A B C D
49. 49. Practice Problems <ul><li>c. If the ray is incident on surface BC , from which surface and at what angle will the ray leave the block? </li></ul><ul><li>Recall: </li></ul><ul><li>Angle of incidence = 60 o </li></ul><ul><li>Angle of refraction = 32.3 o </li></ul><ul><li>Critical angle = 38.1 o </li></ul>Draw refracted ray2. Measure angle of ray2 hitting block. Angle is greater than critical angle of 38.1 o thus ray3 will reflect. Draw ray3 following Law of Reflection. Measure angle of ray3. Since it is the same angle as ray2, it will refract out at the same angle. Thus ray4 refracts at 60 o from surface AD . 30  A B C D 32.3  57.7  32.3  60 
50. 50. Practice Problems <ul><li>Which of the following angles is the critical angle of glass? </li></ul>A B D C
51. 51. Practice Problems <ul><li>Which of the following angles is the critical angle of glass? </li></ul>A B D C
52. 52. <ul><li>A horizontal light ray hits a prism as shown. </li></ul><ul><li>What happens to the light ray? </li></ul>Practice Problems 45  A B C
53. 53. <ul><li>A horizontal light ray hits a prism as shown. </li></ul><ul><li>What happens to the light ray? </li></ul>Practice Problems 45  A B C